How to extrude a bone using Blender's Python API?
It turns out it is not hard to do this using Python. I did it using the following instead:

newBoneLocation = (1, 1.5, 1.2)

bpy.ops.armature.extrude_move(ARMATURE_OT_extrude={"forked":False}, 
TRANSFORM_OT_translate={"value":newBoneLocation, 
"constraint_axis":(False, False, False), 
"constraint_orientation":'GLOBAL', 
"mirror":False, 
"proportional":'DISABLED', 
"proportional_edit_falloff":'SMOOTH', 
"proportional_size":1, 
"snap":False, 
"snap_target":'CLOSEST', 
"snap_point":(0, 0, 0), 
"snap_align":False, 
"snap_normal":(0, 0, 0), 
"gpencil_strokes":False, 
"texture_space":False, 
"remove_on_cancel":False, 
"release_confirm":False, 
"use_accurate":False}`